A Fredholm operator approach to Morita equivalence |
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Authors: | Ruy Exel |
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Affiliation: | (1) Department of Mathematics and Statistics, University of New Mexico, 87131 Albuquerque, NM, USA |
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Abstract: | GivenC*-algebrasA andB and an imprimitivityA-B-bimoduleX, we construct an explicit isomorphismX*:Ki(A)Ki(B), whereKi denotes the complexK-theory functors fori=0, 1. Our techniques do not require separability nor the existence of countable approximate identities. We thus extend to generalC*-algebras the result of Brown, Green, and Rieffel according to which, strongly Morita equivalentC*-algebras have isomorphicK-groups. The method employed includes a study of Fredholm operators on Hilbert modules.On leave from the University of São Paulo, Brazil. |
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Keywords: | Strong Morita equivalence Hilbert modules Fredholm operators sigma-unitalC*-algebras |
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